Word Problem

Question

Two high-speed ferries leave at the same time from a city to go to the same island. The first ferry, the Cat, travels at 34 miles per hour. The second ferry, the Bird, travels at 27 miles per hour. In how many hours will the two ferries be 14 miles apart? 

Answer 1

v1 = speed of Cat = 34 mph

 

v2 = speed of Bird = 27 mph

 

t = ?

 

delta_d = v1*t - v2*t = (v1 -v2)t 

 

14 = (34 - 27)t = 7t

 

t = 14/7 hrs = 2 hrs

Answer 2

You can set up an equation to find the answer to this question, making the left represent the distance the Cat has traveled in terms of time, and the right side the distance the Bird has traveled in terms of time.

 

Let's look at each individual distance equation and then combine them into one.

 

In general, Distance equals rate x time, or D=RT

 

So for the Cat...

 

D = 34*t

 

For the Bird...

 

D = 27*t

 

Now, we want to find when the Cat, which travels faster, is 14 miles ahead of the Bird. So in other words, when the distance the Bird has traveled plus 14 miles is the same as the Cat's distance traveled.

 

So we would make the equation...

 

34*t=27*t+14

 

Solving for this equation will give us how much time (or t in the equation) will have passed when the Bird would have to make up 14 miles to be equal to the Cat, which is what the question is looking for. (Alternatively, 34*t-14=27*t would also work for the same reasons, only this time we'd be finding the time that has passed when, if you moved the Cat backwards 14 miles, it would be at the same point as the Bird. But these two equations are equivalent, which you can see by simply moving the 14 to different sides of equation).

 

So now we solve it.

 

34t=27t+14

 

7t=14

 

t=2

 

So after two hours, the trains will be 14 miles apart.